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There are many ratios that form a proportion 5/7. For instance: 5/7 = 10/14 So any ratio that forms a proportion with 5 over 7 is 5k1/(7k2) where k1 = k2, and k1, k2 are any real values.
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The standard form of a linear equation in two variables, x and y, isax + by = k1 where a, b and k1 are constants.This can be extended to three dimensions (x, y and z) simply:ax + by + cz = k2 where a, b, c and k2 are constants.Extension to 4 or more dimensions can be carried out in a similar way.Apart from the fact that this form lends itself to simple extension to multi-dimensional space, the other main advantage is that the form is easy to represent in matrix form:Thus AX = K where A is the matrix of coefficients, X the matrix of variables and k the matrix of constants. The tools of matrix algebra can then be used to work with these lines in hyperspace.The standard form is sometimes confused with the slope-intercept formy = ax + b.